The supergravity model used in [1]} to discuss the KKLT model is the model in their Sec. 4.2 with two propagating unconstrained superfields \(X, T\)  in addition to a superfield \(\rho \)  representing the volume of the extra dimensions. The KKLT supergravity model in \(M_{Pl}=1\)  units is [2]}
\(K = - 3\ln (\rho +\bar{\rho }) +X^2\, , \qquad W= fX + W_0 + A e^{ -a\rho }\, , \qquad X^2 =0 \ .\) 
